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Spacings around and order statistic

Nagaraja, H. N.; Bharath, Karthik; Zhang, Fangyuan

Authors

H. N. Nagaraja

Fangyuan Zhang



Abstract

We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic Xk:n of a random sample of size n from a continuous distribution F. For central and intermediate cases, normalized spacings in the left and right neighborhoods are asymptotically i.i.d. exponential random variables. The associated independent Poisson arrival processes are independent of Xk:n. For an extreme Xk:n, the asymptotic independence property of spacings fails for F in the domain of attraction of Fréchet and Weibull (α≠1) distributions. This work also provides additional insight into the limiting distribution for the number of observations around Xk:n for all three cases.

Citation

Nagaraja, H. N., Bharath, K., & Zhang, F. (2015). Spacings around and order statistic. Annals of the Institute of Statistical Mathematics, 67(3), https://doi.org/10.1007/s10463-014-0466-9

Journal Article Type Article
Acceptance Date Apr 26, 2014
Online Publication Date Apr 26, 2014
Publication Date Jun 30, 2015
Deposit Date Jun 19, 2017
Publicly Available Date Jun 19, 2017
Journal Annals of the Institute of Statistical Mathematics
Print ISSN 0020-3157
Electronic ISSN 1572-9052
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 67
Issue 3
DOI https://doi.org/10.1007/s10463-014-0466-9
Keywords Spacings; uniform distribution; central order statistics; intermediate order statistics; extremes; Poisson process.
Public URL http://eprints.nottingham.ac.uk/id/eprint/43597
Publisher URL https://link.springer.com/article/10.1007%2Fs10463-014-0466-9
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-014-0466-9.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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